def test_multiply_complex(self):
x, y = MVPolyDict.variables(2, dtype = complex)
p = (x + y)*(x + 1j*y)
q = x**2 + (1 + 1j)*x*y + 1j*y**2
self.assertTrue(p == q,
"bad multiply:\n{0!s}\n{1!s}".format(repr(p.coef),
repr(q.coef)))
def test_nonzero_enumerate(self):
x, y = MVPolyDict.variables(2)
p = 3*x + y**2 + 7
obt = p.nonzero
exp = [((), 7.0), ((1,), 3.0), ((0, 2), 1.0)]
self.assertTrue(sorted(obt) == sorted(exp),
"nonzero")
def test_multiply_arithmetic(self):
x, y = MVPolyDict.variables(2, dtype = int)
p = (x + y)*(2*x - y)
q = 2*x**2 + x*y - y**2
self.assertTrue(p == q,
"bad multiply:\n{0!s}\n{1!s}".format(repr(p.coef),
repr(q.coef)))
def test_construct_from_variables_zero_coefs(self):
x, y = MVPolyDict.variables(2)
p = 0*x + 0*y + 0
exp = {}
obt = p.coef
self.assertTrue(exp == obt,
"bad constructor:\n{0!s} {1!s}".format(repr(obt), repr(exp)))
def bernstein(cls, i, n, **kwargs):
"""
Return the output of :meth:`mvpoly.dict.MVPolyDict.bernstein`
converted to other polynomial subclasess.
"""
from mvpoly.dict import MVPolyDict
return cls(MVPolyDict.bernstein(i, n, **kwargs), **kwargs)
def bell_partial(cls, n, k, **kwargs):
"""
Return the output of :meth:`mvpoly.dict.MVPolyDict.bell_partial`
converted to other polynomial subclasess.
"""
from mvpoly.dict import MVPolyDict
return cls(MVPolyDict.bell_partial(n, k, **kwargs), **kwargs)
def test_diff_invariant(self):
x, y = MVPolyDict.variables(2, dtype = int)
p = x + 2*y
exp = p.coef.copy()
q = p.diff(1,0)
obt = p.coef
self.assertTrue(exp == obt,
"polynomial modified by diff {0!s}".format( \
(repr(obt))))
def test_construct_from_variables(self):
x, y = MVPolyDict.variables(2)
p = x + 2*y + 3
exp = {((0, 1),) : 1,
((1, 1),) : 2,
() : 3}
obt = p.coef
self.assertTrue(exp == obt,
"bad constructor:\n{0!s} {1!s}".format(repr(obt), repr(exp)))
def test_monomials_linear(self):
L = MVPolyDict.monomials(2, 1)
self.assertTrue(len(L) == 3,
"expected 3 monomials, got {0:d}".format(len(L)))
E = [
{ () : 1 },
{ ((0, 1),) : 1 },
{ ((1, 1),) : 1 }
]
for i in range(3):
self.assertTrue(L[i].coef == E[i],
"{0!s} != {1!s}".format(repr(L[i].coef), repr(E[i])))
def test_euler_goldbach(self):
"""
Euler's four-square identity, discussed in 1749 in a letter
from Euler to Goldbach.
"""
a1, a2, a3, a4, b1, b2, b3, b4 = MVPolyDict.variables(8, dtype = int)
p = (a1**2 + a2**2 + a3**2 + a4**2) * (b1**2 + b2**2 + b3**2 + b4**2)
q = (a1*b1 - a2*b2 - a3*b3 - a4*b4)**2 + \
(a1*b2 + a2*b1 + a3*b4 - a4*b3)**2 + \
(a1*b3 - a2*b4 + a3*b1 + a4*b2)**2 + \
(a1*b4 + a2*b3 - a3*b2 + a4*b1)**2
self.assertTrue(p == q,
"bad multiply:\n{0!s}\n{1!s}".format(repr(p.coef),
repr(q.coef)))
def test_monomials_quadratic(self):
L = MVPolyDict.monomials(2, 2)
self.assertTrue(len(L) == 6,
"expected 6 monomials, got {0:d}".format(len(L)))
E = [
{ () : 1 },
{ ((0, 1),) : 1 },
{ ((1, 1),) : 1 },
{ ((0, 2),) : 1 },
{ ((0, 1), (1, 1)) : 1 },
{ ((1, 2),) : 1 },
]
for i in range(5):
self.assertTrue(L[i].coef == E[i],
"{0!s} != {1!s}".format(repr(L[i].coef), repr(E[i])))
def setUp(self):
x, y = MVPolyDict.variables(2, dtype=int)
self.p = self.makep(x, y)
self.x = [1, 1, -1, 0, 7, 3, -3, 1]
self.y = [1, 0, 0, 3, -1, 2, -10, 2]
self.n = len(self.x)
def test_monomials_constant(self):
L = MVPolyDict.monomials(2, 0)
self.assertTrue(L[0].coef == { () : 1 },
"{0!s}".format(repr(L[0].coef)))
